Re: Taylor series expansion

*Subject*: [mg2575] Re: [mg2500] Taylor series expansion*From*: moorep at MARSHALL.EDU (Phil Moore)*Date*: Tue, 21 Nov 1995 09:26:02 -0500*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: Wolfram Research, Inc.

On Wed, 15 Nov 1995, Peter Joseph Onesti wrote: > > Hello, > > Can anyone tell me how I can expand in a Taylor series a function like > Sin[constants+x^m] about x=0 for non-integer values of m? Also, how does > one specify m to be an integer only? > > Thanks in advance, > P. J. Onesti > > I'm assuming that you are asking how to do it in Mathematica, not the pencil and paper method. There is a function called Series. I haven't looked into it very much, but, from the examples in the book, it allows negative integer powers of x. I wrote a function for Talyor polynomials: taylor[func_,a_,n_] = Sum[ D[(func[x],{x,i}]/. x->a)/(i!)*(x-a)^i,{i,0,n}] (* This is the standard formula found in books *) This has some drawbacks. First, x cannot be defined prior to calling taylor. Second, it does not tell you what the general term of the taylor series is, though you can certainly call talyor[f,0,20] and try to see the pattern.